Solve the following equation

Explanation

First we will use a property of equality to isolate the variable term on one side of the equation.  Then we will use a second property of equality to isolate the variable itself.  To solve the original equation, we want to find a simpler equivalent equation of the form a number = s, whose solution is obvious.

Solution

On the right side of the equation, 5 is multiplied by -5, and then 60 is subtracted from the product.  To isolate s, we undo the operations in the opposite order.

• To isolate the variable term, -5s, we add 60 to both sides to undo the subtraction of 60.
• To isolate the variable, s, we divide both sides by -5 to undo the multiplication by -5.

• This is the equation to solve.  First, we want to isolate the variable term, -5s
  • 10 = -5s - 60
• Use the addition property of equality: Add 60 to both sides to isolate -5s
  • 10 + 60 = -5s - 60 + 60
• Do the additions: 10 + 60 = 70 and -60 + 60 = 0.  Now we want to isolate the variable, s.
  • 70 = -5s
• use the division property of equality.  Divide both sides by -5 to isolate s.
  • \(\frac{70}{-5} = \frac{-5s}{-5}\)
• On the left side, do the division.  The quotient of a positive and a negative number is negative.  On the right side, simplify:  \(\require{cancel} \frac{\cancel{5}^1s}{\cancel{5}_1} = s\)
  • -14 = s

Substitute -14 in the original equation to check that it is the correct solution